- Email: [email protected]
All-optical XOR and OR logic gates based on line and point defects in 2-D photonic crystal
Optics & Laser Technology 78 (2016) 139–142
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
All-optical XOR and OR logic gates based on line and point defects in 2-D photonic crystal Kiyanoosh Goudarzi a, Ali Mir a,n, Iman Chaharmahali b, Dariush Goudarzi c a
Faculty of Engineering, Lorestan University, Khoram-Abad, Iran Faculty of Engineering, Islamic Azad University, Andimeshk Branch, Andimeshk, Iran c Faculty of Engineering, Islamic Azad University, Borujerd Branch, Borujerd, Iran b
art ic l e i nf o
a b s t r a c t
Article history: Received 2 July 2015 Received in revised form 27 September 2015 Accepted 18 October 2015
In this paper, we have proposed an all-optical logic gate structure based on line and point defects created in the two dimensional square lattice of silicon rods in air photonic crystals (PhCs). Line defects are embedded in the ГX and ГZ directions of the momentum space. The device has two input and two output ports. It has been shown analytically whether the initial phase difference between the two input beams is π/2, they interfere together constructively or destructively to realize the logical functions. The simulation results show that the device can acts as a XOR and an OR logic gate. It is applicable in the frequency range of 0–0.45 (a/λ), however we set it at (a/λ ¼) 0.419 for low dispersion condition, correspondingly the lambda is equal to 1.55 mm. The maximum delay time to response to the input signals is about 0.4 ps, hence the speed of the device is about 2.5 THz. Also 6.767 dB is the maximum contrast ratio of the device. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Photonic crystal waveguide Defect Phase difference Logic gate
1. Introduction
2. Structure design
Photonic crystals (PhCs) are duality of solid state crystals and have many properties like that. They were discovered in 1987 [1,2]. The most important property of the PhCs is photonic band gap (PBG that creates many applications such as polarization beam splitter [3], waveguides [4], self-collimation beams [5–9], defects [6–8] and all-optical logic gates [8–13] for PhC structures. Defects in the PhCs make localized modes in PBG and occasion incident light propagates with almost no diffraction along a definite direction in PhC waveguides. All-optical logic gates which based on PhC waveguides are basic devices in new optical digital integrated circuits and in all-optical signal processing devices. The objective of this paper is studying of phase difference between beams, responsible of constructive or destructive interference of the lights in the optical logic gates and control of light by defects in the PhC waveguide. In that way, logic gates will be designed with PhC waveguides in two dimensional square lattice of dielectric rods in the air. Here, we used the line and point defects to accommodate our purpose to design logic gates. The device has two input and two output ports. By applying phase difference between beams, we could control the light to output ports. According to the results, we will realize that the proposed device has a performance like a XOR and an OR logic gate.
The equations govern photonic crystals are Maxwell equations. Due to periodic permittivity in two dimensions (ε(x, y)), solving the equations are almost complicated, so we use numerical methods such as the Finite-Difference Time-Domain (FDTD) [14] and the Plane Wave Expansion (PWE) [15,16] to simulate the logic gates. The proposed device is shown in Fig. 1. It consist of two input ports, A and B, and two output ports, O1 and O2 with 18a 18a of 2D square lattice PhC composed of silicon (Si) rods in air, where “a” is the lattice constant. Rods dielectric constant, ε, is 11.56 (n ¼3.4) and their radius is 0.35a. To realize the all-optical logic gates, two types of defects have used as shown in Fig. 1. Line defects are created by removing the rods in ΓX and XM directions as shown in Fig. 1. Point defects are some rods that shown with yellow and blue colors in the Fig. 1. Blue rods have a radius equal to 0.27a and employed to divide the intensity of electrical field in two paths base on Fig. 2. Yellow rod causes phase difference between beams equal π/2 as explained as follow. We utilized the PWE method to calculate and plot the PBG of the structure as shown in Fig. 3. As shown in Fig. 3 there are two localized mode between 0.39–0.425 (a/λ), so we choose the frequency a/λ ¼0.419 as shown in Fig. 2. Because of the fact that in this frequency the slope's curve of PBG is constant, in the ГX and XM direction, the light can propagate in the line defects with minimum scattering. To set the lambda of inputs port to 1.55 mm, we selected a, the lattice constant of the structure, equal to 0.65 mm.
n
Corresponding author. E-mail address: [email protected] (A. Mir).
http://dx.doi.org/10.1016/j.optlastec.2015.10.013 0030-3992/& 2015 Elsevier Ltd. All rights reserved.
140
K. Goudarzi et al. / Optics & Laser Technology 78 (2016) 139–142
Fig. 1. Schematic diagram and direction of the defects according to the first Brillion zone of the proposed all optical logic gate device. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 3. TE band structure of the device, (a): before creation the defects, (b): after creation the defects. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
so we can conclude that the powers are:
Po1 =
⎛ ϕ − ϕ2 π⎞ O1 2 2 uE 2 = + ⎟ cos2 ⎜ − 1 S S 2 4⎠ ⎝
uE 2 ⎡ ⎣ 1 + sin ( ϕ1 − ϕ2 ) ⎤⎦ S ⎛ϕ −ϕ π⎞ O 2 2 uE 2 2 + ⎟ Po2 = 2 = cos2 ⎜ 1 2 4⎠ S S ⎝ =
Fig. 2. Normalized power based on point defect's rods as shown in blue color in Fig.1. Black curve shows coupled light to device (CLD). Red curve shows transmission light (T). Green light curve shows anti reflection light (AR). Blue curve shows reflection light (R). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3. Theoretical methods and simulation results The intensities of the lights at the two output ports of the device, based on the theory of interference, can be obtained as the following form [7]:
⎛ ϕ − ϕ2 π⎞ + ⎟ Io1 = O1 2 = 2 uE 2 cos2 ⎜ − 1 ⎝ 2 4⎠ = uE 2 ⎡⎣ 1 + sin ( ϕ − ϕ ) ⎤⎦ 1
2
⎛ ϕ − ϕ2 π⎞ + ⎟ Io2 = O2 2 = 2 uE 2 cos2 ⎜ 1 ⎝ 2 4⎠ = uE 2 ⎡⎣ 1 − sin ( ϕ1 − ϕ2 ) ⎤⎦
(1)
=
uE 2 ⎡ ⎣ 1 − sin ( ϕ1 − ϕ2 ) ⎤⎦ S
(2)
Where φ1 φ2 is phase difference between beams in input ports A, B and φ1, φ2 are real, E represents a plane wave and u is a function with the same periodicity as the PhC. Io1 and Io2 are intensity of electrical field in output ports O1 and O2 respectively. Po1 and Po2 are power in output ports O1 and O2 respectively and S is cross section of the device at outputs. From Eq. (2) we can see if φ1 φ2 ¼ 2kπ þ π/2 then Io1 ¼ 2|uE|2, Io2 ¼“0” and if φ1 φ2 ¼ 2kπ π/2 then Io2 ¼2|uE|2, Io1 ¼“0”, where k is an integer. Considering k equal to zero then φ1 φ2 ¼ 7 π/2. Therefore, we used the following equation to create a phase difference equal to 7 π/2 [17]:
Δϕ =
2π 4π Δn × 2r = r Δn λ0 λ0
(3)
K. Goudarzi et al. / Optics & Laser Technology 78 (2016) 139–142
Table 1 Truth table and needed phase difference between two input beams to create a XOR and an OR logic gate when the yellow rod is embedded in the port B. φ1 φ2
Input A
Input B
Output O1 (XOR)
Output O2 (OR)
þπ/2 þπ/2 þπ/2 þπ/2
0 0 1 1
0 1 0 1
0 1 1 0
0 1 1 1
141
In Eq. (3), λ0 is the incident wavelength and “r” is the radius of the point defect, Δn is the difference of refraction index between the medium path and the background and Δφ is the created phase delay. According to Eq. (3) we can apply φ1 φ2 ¼ þ π/2 by localizing a rod in the entrance of port B and varying the refraction index of the rod to nearly 2 as shown in Fig. 1 in yellow color. Vice versa we can establish similar condition by set the yellow rod in the entrance of the port A, as shown in Fig. 5, so according to Table 1 and Fig. 4 we have designed the XOR logic gate in the
Fig. 4. The FDTD simulation results of designed XOR and OR logic gates, (a): The logic value of the two input ports, A and B, are “1”, the output port O1 is “0” and O2 is “1”, (b): A is “1”, B is “0”, the output O1 ¼“1” and output O2 ¼ “1”, (c): A is “0”, B is “1”, the two outputs are “1”. The monitor values are shown under the FDTD simulation too. The blue line: power transmission at output O2, the red line: power transmission at output O1, the green line: coupled light to the device (the all values are normalized by the power with 2 mw value). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Table 2 The powers of all optical OR and XOR logic gates when the yellow rod is embedded in the input port B. φ1 φ2
Input A
Input B
Output O1 (XOR)
Output O2 (OR)
þπ/2 þπ/2 þπ/2 þπ/2
0 0 P0 P0
0 P0 0 P0
0 0.48P0 0.48P0 0
0 0.48P0 0.48P0 1.9P0
maximum delay time to achieve “OR” or “XOR” logic operation is 0.4 ps, so, the operation speed of the device is 2.5 THz.
4. Conclusion A device for optical switches and logic gates with minimum power consumption based on line and point defects in the photonic crystal structure, has been considered and demonstrated. It is applicable in the 0–0.45 frequency range (a/λ) with two input and two output ports. The two input optical waves have wavelengths equal to 1.55 mm, and has been shown if the phase difference between them equal to 7 π/2 the device can operate as a XOR and an OR logic gate. The device has a very simple structure and its speed is near the light velocity, so it is a very suitable device for photonic digital integrated circuits.
References
Fig. 5. Schematic diagram and direction of the defects according to the first Brillion zone of the proposed all optical logic gate device, when yellow rod is relocated from the port “B” to the port “A” to achieve π/2 phase difference between the two input beams. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
output port O1 and the OR logic gate in output port O2. Fig. 4 shows the FDTD simulation of the distribution of electrical field in the device for TE polarization. In that way if A and B is equal to “0” then O1, O2 equal to zero. If A and B is equal to “1”, then O1 ¼“0”, O2 ¼“1” and if A ¼“1”, B ¼“0” or A ¼“0”, B ¼“1” then O1, O2 are equal to “1”, so we have XOR in port O1 and OR in port O2. Table 2 shows the power of the all-optical logic gates. We can change the location of yellow rod from input port A to input port B to achieve π/2 phase difference between beams as shown in Fig. 5, then like aforementioned, O1 acts as an OR and O2 acts as a XOR logic gate. Based on the calculations and simulations it can be found that the optical power less than 0.2P0 can be considered as “0” logic value and optical power greater than or equal to 0.3P0 as “1” logic value. According to the contrast ratio equation, 6.767 dB is the maximum contrast ratio for the proposed device. Also the
[1] E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electrons, Phys. Rev. Lett. 58 (1987) 2059. [2] S. John., Strong localization of phonics in certain disordered dielectric superlattice, Phys. Rev. Lett. 58 (1987) 2486. [3] X. Chen, Z. Qiang, D. Zhao, Y. Wang, H. Li, Y. Qiu, W. Zhou, Polarization beam splitter based on photonic crystal self–collimation Mach–Zehnder interferometer, Opt. Commun. 284 (2011) 490–493. [4] E. Mehmet Bayindir, I. Cubukcu, T. Bulu, E. Tut, C.M. Soukoulis, Photonic band gaps, defect characteristics, and waveguiding in two–dimensional disordered dielectric and metallic photonic crystals, Phys. Rev. B 64 (2001) 195113. [5] S.G. Lee, S.S. Oh, J.E. Kim, H.Y. Yong Park, Line–defect–induced bending and splitting of self–collimated beam in two–dimensional photonic crystals, Appl. Phys. Lett. 87 (2005) 181106. [6] Y. Zhu, H.J. Yang, Applications of self-collimated properties of photonic crystal in 3D imaging lidar system, J. Electron. Sci. Technol. 9 (1) (2011) 78–80. [7] C.S. Kee, D.K. Ko, J. Lee, Self–collimated beams in two–dimensional photonic crystals: properties and applications, J. Korean Phys. Soc. 51 (4) (2007) 1479–1483. [8] Y. Zhang, Y. Zhang, B. Li, Optical switches and logic gates based on self-collimated beams in two–dimensional photonic crystals, Opt. Express 15 (2007) 9287–9292. [9] X. Susan, A. Christina, P. Kabilan, Design of optical logic gates using self-collimated beams in 2D photonic crystal, Photonic Sens. 2 (2) (2012) 173–179. [10] C. Husko, T.D. Vo, B. Corcoran, J. Li, T.F. Krauss, B.J. Eggleton, Ultracompact alloptical XOR logic gate in a slow-light silicon photonic crystal waveguide, Opt. Express 19 (21) (2011) 20681–20690. [11] K. Yi Lee, C.H. Yang, Y.J. Lin, W.Y. Lee, C.C. Lee, S.H. Wong, The designs of 4 2 encoder based on photonic crystals, SPIE–OSA–IEEE/, vol. 7630, 2009, pp. 76300I1–76300I–7. [12] K.Y. Lee, V.P. Yang, I.C. Yang, V.L. Tsai, H.F. Liao, Y.J. Lin, W.L. Lee, Y.T. Tsai, Optical logic operation for AND gate based on planar photonic crystal circuit, SPIE-OSA-IEEE/, vol. 8308, 2011, pp. 83081S–1–83081S–6. [13] M. Ali, M. Birjandi, M. Ghadrdan, All–optical ultra-compact photonic crystal switch based on nonlinear micro ring resonators, Int. Res. J. Appl. Basic Sci. 4 (4) (2013) 972–975. [14] K.S. Kunz, R.J. Luebbers, The Finite Difference Time Domain Method for Electromaganetics, CRC Press, Boca Raton, FL, 1993. [15] K.M. Leung, Y.F. Liu, Photon band structures: the plane–wave method, Phys. Rev. B 41 (1990) 10188. [16] K.M. Ho, C.T. Chan, C.M. Soukouils, Existence of a photonic gap in periodic dielectric structures, Phys. Rev. Lett. 65 (1990) 3152. [17] Protopopov Vladimir, Practical Opto-Electronics; An Illustrated Guide for the Laboratory, Springer Series in Optical Sciences, USA, 2014.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
All-optical XOR and OR logic gates based on line and point defects in 2-D photonic crystal Kiyanoosh Goudarzi a, Ali Mir a,n, Iman Chaharmahali b, Dariush Goudarzi c a
Faculty of Engineering, Lorestan University, Khoram-Abad, Iran Faculty of Engineering, Islamic Azad University, Andimeshk Branch, Andimeshk, Iran c Faculty of Engineering, Islamic Azad University, Borujerd Branch, Borujerd, Iran b
art ic l e i nf o
a b s t r a c t
Article history: Received 2 July 2015 Received in revised form 27 September 2015 Accepted 18 October 2015
In this paper, we have proposed an all-optical logic gate structure based on line and point defects created in the two dimensional square lattice of silicon rods in air photonic crystals (PhCs). Line defects are embedded in the ГX and ГZ directions of the momentum space. The device has two input and two output ports. It has been shown analytically whether the initial phase difference between the two input beams is π/2, they interfere together constructively or destructively to realize the logical functions. The simulation results show that the device can acts as a XOR and an OR logic gate. It is applicable in the frequency range of 0–0.45 (a/λ), however we set it at (a/λ ¼) 0.419 for low dispersion condition, correspondingly the lambda is equal to 1.55 mm. The maximum delay time to response to the input signals is about 0.4 ps, hence the speed of the device is about 2.5 THz. Also 6.767 dB is the maximum contrast ratio of the device. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Photonic crystal waveguide Defect Phase difference Logic gate
1. Introduction
2. Structure design
Photonic crystals (PhCs) are duality of solid state crystals and have many properties like that. They were discovered in 1987 [1,2]. The most important property of the PhCs is photonic band gap (PBG that creates many applications such as polarization beam splitter [3], waveguides [4], self-collimation beams [5–9], defects [6–8] and all-optical logic gates [8–13] for PhC structures. Defects in the PhCs make localized modes in PBG and occasion incident light propagates with almost no diffraction along a definite direction in PhC waveguides. All-optical logic gates which based on PhC waveguides are basic devices in new optical digital integrated circuits and in all-optical signal processing devices. The objective of this paper is studying of phase difference between beams, responsible of constructive or destructive interference of the lights in the optical logic gates and control of light by defects in the PhC waveguide. In that way, logic gates will be designed with PhC waveguides in two dimensional square lattice of dielectric rods in the air. Here, we used the line and point defects to accommodate our purpose to design logic gates. The device has two input and two output ports. By applying phase difference between beams, we could control the light to output ports. According to the results, we will realize that the proposed device has a performance like a XOR and an OR logic gate.
The equations govern photonic crystals are Maxwell equations. Due to periodic permittivity in two dimensions (ε(x, y)), solving the equations are almost complicated, so we use numerical methods such as the Finite-Difference Time-Domain (FDTD) [14] and the Plane Wave Expansion (PWE) [15,16] to simulate the logic gates. The proposed device is shown in Fig. 1. It consist of two input ports, A and B, and two output ports, O1 and O2 with 18a 18a of 2D square lattice PhC composed of silicon (Si) rods in air, where “a” is the lattice constant. Rods dielectric constant, ε, is 11.56 (n ¼3.4) and their radius is 0.35a. To realize the all-optical logic gates, two types of defects have used as shown in Fig. 1. Line defects are created by removing the rods in ΓX and XM directions as shown in Fig. 1. Point defects are some rods that shown with yellow and blue colors in the Fig. 1. Blue rods have a radius equal to 0.27a and employed to divide the intensity of electrical field in two paths base on Fig. 2. Yellow rod causes phase difference between beams equal π/2 as explained as follow. We utilized the PWE method to calculate and plot the PBG of the structure as shown in Fig. 3. As shown in Fig. 3 there are two localized mode between 0.39–0.425 (a/λ), so we choose the frequency a/λ ¼0.419 as shown in Fig. 2. Because of the fact that in this frequency the slope's curve of PBG is constant, in the ГX and XM direction, the light can propagate in the line defects with minimum scattering. To set the lambda of inputs port to 1.55 mm, we selected a, the lattice constant of the structure, equal to 0.65 mm.
n
Corresponding author. E-mail address: [email protected] (A. Mir).
http://dx.doi.org/10.1016/j.optlastec.2015.10.013 0030-3992/& 2015 Elsevier Ltd. All rights reserved.
140
K. Goudarzi et al. / Optics & Laser Technology 78 (2016) 139–142
Fig. 1. Schematic diagram and direction of the defects according to the first Brillion zone of the proposed all optical logic gate device. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 3. TE band structure of the device, (a): before creation the defects, (b): after creation the defects. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
so we can conclude that the powers are:
Po1 =
⎛ ϕ − ϕ2 π⎞ O1 2 2 uE 2 = + ⎟ cos2 ⎜ − 1 S S 2 4⎠ ⎝
uE 2 ⎡ ⎣ 1 + sin ( ϕ1 − ϕ2 ) ⎤⎦ S ⎛ϕ −ϕ π⎞ O 2 2 uE 2 2 + ⎟ Po2 = 2 = cos2 ⎜ 1 2 4⎠ S S ⎝ =
Fig. 2. Normalized power based on point defect's rods as shown in blue color in Fig.1. Black curve shows coupled light to device (CLD). Red curve shows transmission light (T). Green light curve shows anti reflection light (AR). Blue curve shows reflection light (R). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3. Theoretical methods and simulation results The intensities of the lights at the two output ports of the device, based on the theory of interference, can be obtained as the following form [7]:
⎛ ϕ − ϕ2 π⎞ + ⎟ Io1 = O1 2 = 2 uE 2 cos2 ⎜ − 1 ⎝ 2 4⎠ = uE 2 ⎡⎣ 1 + sin ( ϕ − ϕ ) ⎤⎦ 1
2
⎛ ϕ − ϕ2 π⎞ + ⎟ Io2 = O2 2 = 2 uE 2 cos2 ⎜ 1 ⎝ 2 4⎠ = uE 2 ⎡⎣ 1 − sin ( ϕ1 − ϕ2 ) ⎤⎦
(1)
=
uE 2 ⎡ ⎣ 1 − sin ( ϕ1 − ϕ2 ) ⎤⎦ S
(2)
Where φ1 φ2 is phase difference between beams in input ports A, B and φ1, φ2 are real, E represents a plane wave and u is a function with the same periodicity as the PhC. Io1 and Io2 are intensity of electrical field in output ports O1 and O2 respectively. Po1 and Po2 are power in output ports O1 and O2 respectively and S is cross section of the device at outputs. From Eq. (2) we can see if φ1 φ2 ¼ 2kπ þ π/2 then Io1 ¼ 2|uE|2, Io2 ¼“0” and if φ1 φ2 ¼ 2kπ π/2 then Io2 ¼2|uE|2, Io1 ¼“0”, where k is an integer. Considering k equal to zero then φ1 φ2 ¼ 7 π/2. Therefore, we used the following equation to create a phase difference equal to 7 π/2 [17]:
Δϕ =
2π 4π Δn × 2r = r Δn λ0 λ0
(3)
K. Goudarzi et al. / Optics & Laser Technology 78 (2016) 139–142
Table 1 Truth table and needed phase difference between two input beams to create a XOR and an OR logic gate when the yellow rod is embedded in the port B. φ1 φ2
Input A
Input B
Output O1 (XOR)
Output O2 (OR)
þπ/2 þπ/2 þπ/2 þπ/2
0 0 1 1
0 1 0 1
0 1 1 0
0 1 1 1
141
In Eq. (3), λ0 is the incident wavelength and “r” is the radius of the point defect, Δn is the difference of refraction index between the medium path and the background and Δφ is the created phase delay. According to Eq. (3) we can apply φ1 φ2 ¼ þ π/2 by localizing a rod in the entrance of port B and varying the refraction index of the rod to nearly 2 as shown in Fig. 1 in yellow color. Vice versa we can establish similar condition by set the yellow rod in the entrance of the port A, as shown in Fig. 5, so according to Table 1 and Fig. 4 we have designed the XOR logic gate in the
Fig. 4. The FDTD simulation results of designed XOR and OR logic gates, (a): The logic value of the two input ports, A and B, are “1”, the output port O1 is “0” and O2 is “1”, (b): A is “1”, B is “0”, the output O1 ¼“1” and output O2 ¼ “1”, (c): A is “0”, B is “1”, the two outputs are “1”. The monitor values are shown under the FDTD simulation too. The blue line: power transmission at output O2, the red line: power transmission at output O1, the green line: coupled light to the device (the all values are normalized by the power with 2 mw value). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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K. Goudarzi et al. / Optics & Laser Technology 78 (2016) 139–142
Table 2 The powers of all optical OR and XOR logic gates when the yellow rod is embedded in the input port B. φ1 φ2
Input A
Input B
Output O1 (XOR)
Output O2 (OR)
þπ/2 þπ/2 þπ/2 þπ/2
0 0 P0 P0
0 P0 0 P0
0 0.48P0 0.48P0 0
0 0.48P0 0.48P0 1.9P0
maximum delay time to achieve “OR” or “XOR” logic operation is 0.4 ps, so, the operation speed of the device is 2.5 THz.
4. Conclusion A device for optical switches and logic gates with minimum power consumption based on line and point defects in the photonic crystal structure, has been considered and demonstrated. It is applicable in the 0–0.45 frequency range (a/λ) with two input and two output ports. The two input optical waves have wavelengths equal to 1.55 mm, and has been shown if the phase difference between them equal to 7 π/2 the device can operate as a XOR and an OR logic gate. The device has a very simple structure and its speed is near the light velocity, so it is a very suitable device for photonic digital integrated circuits.
References
Fig. 5. Schematic diagram and direction of the defects according to the first Brillion zone of the proposed all optical logic gate device, when yellow rod is relocated from the port “B” to the port “A” to achieve π/2 phase difference between the two input beams. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
output port O1 and the OR logic gate in output port O2. Fig. 4 shows the FDTD simulation of the distribution of electrical field in the device for TE polarization. In that way if A and B is equal to “0” then O1, O2 equal to zero. If A and B is equal to “1”, then O1 ¼“0”, O2 ¼“1” and if A ¼“1”, B ¼“0” or A ¼“0”, B ¼“1” then O1, O2 are equal to “1”, so we have XOR in port O1 and OR in port O2. Table 2 shows the power of the all-optical logic gates. We can change the location of yellow rod from input port A to input port B to achieve π/2 phase difference between beams as shown in Fig. 5, then like aforementioned, O1 acts as an OR and O2 acts as a XOR logic gate. Based on the calculations and simulations it can be found that the optical power less than 0.2P0 can be considered as “0” logic value and optical power greater than or equal to 0.3P0 as “1” logic value. According to the contrast ratio equation, 6.767 dB is the maximum contrast ratio for the proposed device. Also the
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